How can I constrain weights of linear classifier?

Question

There are a number of neurons and we know their firing rates on -3s, -2s, -1s, like

Neuron index:

                  1     2     3     4

Firing rata

         0s:      1     1    -1     1
        -1s:     -1    -1     0    -1
        -2s:      0     0     0     0
        -3s:      1     1     1     1

By using these fire rate history, I want to predict current (0s) firing rate of neurons whether it is 1 or -1. I am using linear SVM and varying weights of each time point.

However, I want to constrain absolute value of weight of recent firing rate is always larger than that of past like

Weight of

-1s: -0.8

-2s: 0.3

-3s: -0.1

How can I realize this idea on linear classifier like linear SVM on MATLAB?

score 2 · Accepted Answer · answered Dec 23 '15 at 07:27

One option is to add a constraint to your optimization problem, that is take a regular SVM problem and add the constraint:

For i=2,3,...,d. This is not an SVM problem anymore, so you'll have to find some general optimization engine or write a solver yourself. Note also that this optimization problem is no longer convex, so any optimization algorithm will only find a local minimum.

How can I constrain weights of linear classifier?

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